I don't think you are being rude or unreasonable at all, OP. It's your house, and therefore, your choice as to who is allowed to come in. Nothing remotely unreasonable about that. The only possible rude thing here is if your delivery was nasty, and it doesn't sound like that at all.
As for me, I would be stressed to have a child in a house that was not child-proof or child-ready at all, let alone while trying to set up for a major party. No thank-you. And as others have pointed out, the friend's DH looking after the child could easily be different to what the OP or other people see as 'looking after'. The child may be allowed to run riot in the house with the father following behind, only there to ensure the child doesn't get hurt, and nothing more (I've seen this a lot). The father may be great and keep the child entertained off quietly in another room, on the other hand. But it is a gamble that one doesn't want to take at the last minute while stressfully preparing for a big annual event.
It sounds like the friend could easily work around this (many people have made good suggestions), but doesn't want to. I feel that this isn't because the friend is being difficult, but rather, it's because she is used to having a toddler around and doesn't realise that other people don't see it as the normal everyday thing that she does. And let's be honest, we're all guilty of this at time in various small areas. Just because we don't see something as a problem, we have difficulty accepting that something so simple and harmless is apparently abhorrent or impossible for others, and can start assuming that they are being silly or something, when in fact, they just don't see the world as we do, and aren't acclimatised to the same types of things.